The invention relates to an electromagnetic switch for starting devices of internal combustion engines. It is already known in the case of such a switch to provide primary current contacts with inclined flat contact surfaces and the contact bridge with correspondingly bent-off ends as contact sections. On closing of the contacts, the contact bridge and primary current contacts should lie against each other over a relatively large area. In this arrangement, it is of disadvantage that in plan view, a rectangular contact bridge requires an anti-rotation means, as otherwise no parallel contact making is possible. Such anti-rotation means is known, for example, in the form of ribs or walls in the cap which carries the primary current contacts and surrounds the switching space. Such anti-rotation means have, however, the disadvantage that, under harsh operational conditions of motor vehicles, vibrations can cause damage by in the cap because of notches therein and/or damage of the contact bridge or its insulating bearing parts, to which additionally the recoil force of the cap wall can contribute. In addition, with the relatively large level contact surfaces, it is of disadvantage that, with a view to a cost-effective mass production, the contact surfaces cannot be made so flat and/or kept so parallel to each other that contact making always takes place in the centre of the contact surfaces. As a result, no uniform heat dissipation is possible, so that the welding tendency of the contact parts increases in an undesired way. The friction on contact making of the contact surfaces inclined with respect to the switching direction can admittedly have the effect that corrosion deposits on the contact surfaces are dislodged and pushed away to a certain extent. With the relatively large contact surfaces, nevertheless it happens again and again that the contact making takes place at poorly conducting or otherwise unfavourable points, because the self-cleaning effect cannot become sufficiently effective here and the, in itself, desired high contact force can, with contact surfaces arranged obliquely to the switching movement, press the impurities into the contact surfaces.